Symmetric with respect to the y-axis
When a shape or function is symmetric with respect to the y-axis, it means that if we were to fold the shape along the y-axis, the two resulting halves would perfectly overlap each other
When a shape or function is symmetric with respect to the y-axis, it means that if we were to fold the shape along the y-axis, the two resulting halves would perfectly overlap each other.
In terms of an equation, if a function is symmetric with respect to the y-axis, it means that substituting -x for x in the equation results in an equivalent expression. Mathematically, this can be represented as:
f(x) = f(-x)
To illustrate this concept, let’s consider the equation of a quadratic function: f(x) = x^2.
If we substitute -x for x in the equation, we get:
f(-x) = (-x)^2 = x^2
As you can see, f(x) and f(-x) are equivalent, which means that the function f(x) = x^2 is symmetric with respect to the y-axis. If you were to graph this function, you would see that the resulting parabola is symmetric about the y-axis.
This concept can also be extended to other shapes, such as geometric figures. For example, if you have a square, you can fold it in half along the y-axis, and the resulting halves will perfectly overlap each other. Similarly, a circle is also symmetric with respect to the y-axis, as folding it along the y-axis would result in both halves overlapping.
So, when something is said to be symmetric with respect to the y-axis, it means that it exhibits a reflectional symmetry where the left and right sides are identical.
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